How images become spatial answers—and what the numbers mean

How does an image become a description of three-dimensional space?

**Takeaway:** AI combines image evidence with geometric constraints or learned estimates to answer a defined spatial question. [1, 18]

The pinhole model constrains the relation between 3D scene/camera coordinates and observed image pixels through camera intrinsics and rotation/translation; this supplies the geometric basis of the synthesis.

How do object shapes and locations become spatial relationships?

The crucial step is matching the quantity to the question: an exact distance between two representative object positions does not measure the gap between their surfaces. [14, 15]

The gateway subtracts resolved p3 positions and computes their Euclidean norm; its default centroid mode is explicitly distinguished from optional reconstructed-cloud closest/farthest modes. This identifies which quantity the representative-position calculation actually computes.

How does an image become a description of three-dimensional space?

For ideal rectified horizontal stereo with the appropriate principal-point convention, \[ Z=fB/d, \] where \(d\) is pixel disparity and \(B\) is the known camera separation. [1, 2]

The tutorial gives disparity=Bf/Z, defines B as known camera separation and obtains disparity from corresponding-image matches.